 • ITA
Category: Credit Rating Methodologies

# Game Theory Approach for Credit Risk Analysis

## How to exactly evaluate a Credit Rating?

One of the first items that need to be studied when assessing the credit risk of a company is the calculation of the financial ratios. In fact, the financial theory tells us what are the ratios that need to be studied and what should be their value for understanding the risk of the company evaluated.

As already written in a previous post (link) the ratios can be divided into different areas of analysis, for example (and with simplicity):

1. Solvency;
2. Liquidity;
3. Profitability.
What will be the company with lower credit risk? Obviously the company with the better ratios.
Unfortunately, this answer is not so easy to define mathematically and unfortunately many researchers in the field of modelling credit risk do not think about that.

In fact, which is the meaning to have better financial ratios?

If X is the company, the various ratios will be: Fi(X), i = 1, .., n where n is the number of calculated ratios.

Without losing precision we can say that company X to be good (high Credit Rating) has to have all ratios maximum:

max Fi(X) = 1, .., n

And here the problems begin: the formulation outlined above is a multi-objective optimization problem!

And how do you solve a multi objective problem? Well, the exact method to solve the above problem is only the use of Game Theory!

So we understand that to develop a model for credit rating evaluation we must necessarily rely on algorithms that can use the Game Theory.
But now we have another problem: what different Game Theory can be used and better suited to our problem?

Even here the answers are not simple, in fact we have several possibilities:
1. Nash;
2. Stackelberg;
3. Pareto;
4. Exc.
Without going in different numerical definitions, our idea is that the Game Theory that best suits the creation of a model for Credit Rating Evaluation is the Pareto Theory.

So the company that has the best credit rating is one that meets the optimum point according to Pareto.

Interesting right?

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